Kinematic equation without time

  • #1
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Main Question or Discussion Point

I understand most of the kinematic equations, but there is just this one equation that omits time from the equation. I always end up with V02+2a(x - x0) = 2V0V + V2

The 2V0V part is what I don't understand how to get rid of. So if you please could you do the equation with steps , I would be very grateful. Thank you.
 

Answers and Replies

  • #2
Ibix
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What are the steps you took to get to that equation?
 
  • #3
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t = (V - V0)/a

x - x0 = V0((V-V0)/a) + .5a((V - V0/a)2)

x - x0 = (V0V - V02)/a + (V2 + V02)/2a

2a(x - x0) = 2V0V -2V02 + V2 +V02

V02+2a(x - x0) = 2V0V + V2
 
  • #4
Ibix
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What do you get if you expand ##(V-V_0)^2##?

Edit: By the way, something seems to be wrong with the brackets in the last term of your second equation. I assumed that was just a typo, but if they look right to you then you need tk think about that too.
 
Last edited:
  • #5
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Oh I see what I did wrong. As you intimated, I did not expand (V - V0)2 correctly. Now I have -2V0V to cancel out.
 
  • #6
Ibix
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That's right. Algebraic slips can be hard to spot. I sometimes write each term on a separate line when I'm expanding brackets, which makes it easier for me to not get distracted when I'm doing it. Then when I'm collecting terms together I put a little tick above each one as I copy it on to the next line so I don't lose one or double one up by accident. You can also count terms. You know that ##(V-V_0)^2## should give you three terms when expanded - that would have caught this error because your expansion only had two.
 

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